While al Qaeda preaches war against non-Moslems, much anger and violence is also directed at fellow Moslems who don't measure up to the religious and moral standards of Islamic fundamentalists. You could say that the al Qaeda attacks on non-Moslems are a distraction from their true mission; to purify  Islamic society. 

Eliminating heretics and enforcing religious purity is nothing new. Every religion has "holier than thou" groups. But in Islam, the tradition of using violence to back a religious position survives more extensively than in the other major religions (Christianity, Hinduism and Judaism). The reason has more to do with politics than religion. Arab nations have never developed a participatory government (democracy) or modern economies. As a result, most Arabs are poor and have no say in how they are ruled. As happened everywhere else, radio, movies and television made large, illiterate, populations aware that there was a different way, a better life, but it was out of reach. Lots of these Arabs are now mad about that. They used to just be mad at their own governments, but then these government did what tyrants have always done, they found someone else to blame for their sins. The blame was put on the West, making much reference to the crusades. That the last crusade took place in 1398, against the Turks, and failed miserably, means nothing when you are trying to shift blame. 

The reality is that Arabs have been conquered and ruled by other Moslems (Turks and Iranians) for most of the last five hundred years. The lack of economic success is largely due to cultural factors, just as is the case in Latin America and Africa. That used to be the case in East Asia, but after World War II the people in that region took a close look at the Western economies and did what had to be done. Namely, they established rule of law (you cannot attract a lot of business investment without it) and pushed education (to attract jobs, both high tech and low.) Neither of these policies are pushed in most Moslem, and particularly Arab, nations. This was not really a religious issue, but a cultural one. The people at the top of the economic and power pyramid in these nations felt comfortable with the way things were. Tradition, and all that, plus fear of change. Opponents were bought off (if they were open to a deal and looked like they might succeed), killed or driven into exile. After World War II, nationalism and socialism were popular, but after a lot of republics were set up, with the same old crowd were in charge, running things under the same old rules, popular discontent returned. People wanted a change for the better.

So now the calls for reform in Moslem nations are most energetically pushed by Islamic radicals. Normally, rebellion comes from educated members of the ruling class who disagree with the crowd currently holding the power. While it's been a popular myth that revolution is often led by poverty stricken men, desperate for change, the reality is a core groups of educated rebels mobilizing less well of and less educated men to do most of the dying. If the revolution is successful, the poor generally remain poor, and a new crew of educated, or even upper class, families take over. This is the case with the Islamic revolution in Iran, and al Qaeda. Attacks on non-Arabs in foreign countries are a luxury for these people. 

While it's easier, and seems more practical, to attack the enemies at home, this often does not work. There's a major problem with making war in your home country; you are going to kill some of your potential supporters (oppressed folks like you) as you attack your local tyrants. That's what happened to the Egyptian Moslem Brotherhood in the early 1990s. Some bombing attacks killed some children and public opinion turned against the Brotherhood. With that, it was much easier for the government to round up or drive out most of the Islamic radicals. These exiles went on to form the core of al Qaeda. But they were rebels-without-a-country. 

Al Qaeda thought they could have their own country in Afghanistan, but eventually learned that most Afghans hated them as arrogant foreigners. One reason the Taliban was defeated so quickly, by fewer than three hundred U.S. troops on the ground in late 2001, was that al Qaeda had made themselves, and their Taliban allies, so unpopular in Afghanistan. Faced with an inability to mobilize and control the large number of angry young Moslem men, they are now going after the much smaller subset of this group that are eager to go off and attack foreigners. This sort of thing does nothing for the situation back home, except to get some of the more violent and unstable young men out of the country. Al Qaeda, however, represents part of a much larger discontent in the Arab world. People want a better deal, and don't know how to get it. What's going on in Iraq right now is liable to change all that. No Arab country has ever tried real democracy. In Egypt it's one party democracy where all the old players keep their power and privileges. Lebanon was just a power sharing agreement among traditional groups. If multiparty democracy works in Iraq, and it may not, it will shake the foundations of all other Arab countries. And that is to be feared by those now in power, for it is more than change, it is fundamental change. No one even wants to think about it, so the religious and secular leadership in Arab nations try to distract their people with stories of evil foreigners attempting to poison and control the purity of Arab culture. It's a dangerous game, because so much is at stake. It's also a war where most of the battles are fought with paper bullets, rather than metal ones. And it's a war that can be lost, as has been in the past, which is why the Arab states have failed to get into the 20th century mentally, economically and socially. Eventually, this war will be won, it's just a matter of when.